Textbook Question
A glass rod that has been charged to +12 nC touches a metal sphere. Afterward, the rod’s charge is +8.0 nC. How many charged particles were transferred?
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Ch 22: Electric Charges and Forces
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796
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Table of contents
- Ch 01: Concepts of Motion35
- Ch 02: Kinematics in One Dimension75
- Ch 03: Vectors and Coordinate Systems58
- Ch 04: Kinematics in Two Dimensions60
- Ch 05: Force and Motion23
- Ch 06: Dynamics I: Motion Along a Line53
- Ch 07: Newton's Third Law27
- Ch 08: Dynamics II: Motion in a Plane52
- Ch 09: Work and Kinetic Energy56
- Ch 10: Interactions and Potential Energy50
- Ch 11: Impulse and Momentum56
- Ch 12: Rotation of a Rigid Body71
- Ch 13: Newton's Theory of Gravity52
- Ch 14: Fluids and Elasticity44
- Ch 15: Oscillations55
- Ch 16: Traveling Waves37
- Ch 17: Superposition39
- Ch 18: A Macroscopic Description of Matter53
- Ch 19: Work, Heat, and the First Law of Thermodynamics60
- Ch 20: The Micro/Macro Connection53
- Ch 21: Heat Engines and Refrigerators34
- Ch 22: Electric Charges and Forces40
- Ch 23: The Electric Field39
- Ch 24: Gauss' Law32
- Ch 25: The Electric Potential63
- Ch 26: Potential and Field57
- Ch 27: Current and Resistance42
- Ch 28: Fundamentals of Circuits39
- Ch 29: The Magnetic Field47
- Ch 30: Electromagnetic Induction60
- Ch 31: Electromagnetic Fields and Waves32
- Ch 32: AC Circuits63
- Ch 33: Wave Optics32
- Ch 34: Ray Optics57
- Ch 35: Optical Instruments30
- Ch 36: Special Relativity38
- Ch 37: The Foundations of Modern Physics25
- Ch 38: Quantization49
- Ch 39: Wave Functions and Uncertainty31
- Ch 40: One-Dimensional Quantum Mechanics35
- Ch 41: Atomic Physics18
- Ch 42: Nuclear Physics27
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Not the one you use?Change textbook
Chapter 22, Problem 1
3.5×1010 electrons are added to a plastic rod by rubbing it with wool. What is the charge on the rod?
Verified step by step guidance1
Understand the problem: The charge on the rod is determined by the number of electrons added to it. Each electron carries a fundamental charge of approximately \( -1.6 \times 10^{-19} \; \text{C} \) (Coulombs). The total charge can be calculated by multiplying the number of electrons by the charge of a single electron.
Write the formula for total charge: \( Q = n \cdot e \), where \( Q \) is the total charge, \( n \) is the number of electrons, and \( e \) is the charge of a single electron.
Substitute the given values into the formula: \( n = 3.5 \times 10^{10} \) and \( e = -1.6 \times 10^{-19} \; \text{C} \). The negative sign indicates that electrons carry a negative charge.
Perform the multiplication: Multiply \( 3.5 \times 10^{10} \) by \( -1.6 \times 10^{-19} \) to find the total charge \( Q \). Ensure you handle the powers of 10 correctly by adding their exponents.
Interpret the result: The final value of \( Q \) will represent the total charge on the rod in Coulombs. The negative sign indicates that the charge is negative, as expected for an object gaining electrons.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Charge of an Electron
An electron carries a fundamental unit of electric charge, which is approximately -1.6 × 10^-19 coulombs. This negative charge is essential for understanding how the addition or removal of electrons affects the overall charge of an object, such as the plastic rod in this scenario.
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04:32
Electrons In Water (Using Density)
Conservation of Charge
The principle of conservation of charge states that the total electric charge in an isolated system remains constant. When electrons are added to the plastic rod, the rod becomes negatively charged, while the wool loses an equal amount of negative charge, ensuring that the overall charge is conserved.
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05:43Conservation of Charge
Calculating Total Charge
To find the total charge on the rod after adding electrons, multiply the number of electrons by the charge of a single electron. In this case, the total charge can be calculated as Q = n × e, where n is the number of electrons and e is the charge of one electron, leading to a clear understanding of the rod's net charge.
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05:29Total Internal Reflection
Related Practice
Textbook Question
A plastic rod that has been charged to −15 nC touches a metal sphere. Afterward, the rod's charge is −10 nC. How many charged particles were transferred?
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Textbook Question
A plastic rod that has been charged to −15 nC touches a metal sphere. Afterward, the rod's charge is −10 nC. What kind of charged particle was transferred between the rod and the sphere, and in which direction? That is, did it move from the rod to the sphere or from the sphere to the rod?